# Ultrafast ab-initio Quantum Chemistry Using Matrix Product States

## TL;DR

This paper advances ultrafast quantum chemistry by developing an MPS-based method that efficiently simulates electron dynamics in molecules, achieving near full CI accuracy for femtosecond timescales and aligning well with experimental data.

## Contribution

It introduces a novel combination of MPS with time evolution schemes for simulating ultrafast electron dynamics at a full CI level.

## Key findings

- MPS approach accurately reproduces full CI results for hydrogen chains and water.
- Krylov space time evolution enhances efficiency and flexibility of MPS simulations.
- Application to iodoacetylene matches experimental charge migration observations.

## Abstract

Ultrafast dynamics in chemical systems provide a unique access to fundamental processes at the molecular scale. A proper description of such systems is often very challenging because of the quantum nature of the problem. The concept of matrix product states (MPS), however, has proven its performance in describing such correlated quantum system in recent years for a wide range of applications. In this work, we continue the development of the MPS approach to study ultrafast electron dynamics in quantum chemical systems. The method combines time evolution schemes, such as fourth-order Runge-Kutta and Krylov space time evolution, with MPS, in order to solve the time-dependent Schr\"odinger equation efficiently. This allows for describing electron dynamics in molecules on a full configurational interaction (CI) level for a few femtoseconds after excitation. As a benchmark, we compare MPS based calculations to full CI calculations for a chain of hydrogen atoms and for the water molecule. Krylov space time evolution is in particular suited for the MPS approach, as it provides a wide range of opportunities to be adjusted to the reduced MPS dimension case. Finally, we apply the MPS approach to describe charge migration effects in iodoacetylene and find direct agreement between our results and experimental observations.